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Induced drag - where does it actually arise from?
Several explanations about induced drag exist. Even if these explanations are simple and appealing (and not necessarily correct) they lack any connection to how actually the concept of induced drag has been historically deduced and is practically used.
So, in order to grasp the real meaning of induced drag, I ask (and answer) myself here where this drag term actually arises from?

Related: https://aviation.stackexchange.com/questions/84113/explained-intuitively-why-does-aspect-ratio-affect-induced-drag

Does this answer your question? Do wall-to-wall airfoils produce induced drag?

@RalphJ: I read all the induced-drag-related answers that I found on this Stackexchange and didn't find any showing the physical/mathematical derivation of it, that's why this Q&A of mine. Just a different and maybe more rigorous (but hopefully still easy to follow) point of view

In the answer I'm going to start from the simplest ideal 2D airfoil to the real complete 3D wing, adding one brick at a time. In my opinion this is the best way to introduce the induced drag since induced drag is basically a mathematically well defined drag term that appears only going from 2D to 3D. I'm not going to use any equations here, just a linear-growing explanation of why and how the concept of induced drag was born.
At the end I will also discuss some of the existing "simple and appealing" explanations and I will explain where the name comes from.

Step 1: ideal 2D airfoil

Why do we care about a not-in-reality-existing 2D airfoil? Well because it is the basic building block of any wing. Any wing is built putting airfoils near each other and therefore the behaviour of the whole wing cannot be truly understood until the behaviour of the single airfoil composing it is not understood. Wings of several aircrafts are built around some more or less standard 2D airfoil: just to name a few, F-22 uses NACA 64A005.29, F-16 NACA 64A204, Agusta A109 NACA 23012, Boeing 747 BAC463, Cessna 172 Skyhawk NACA 2412 and so on. And since the behaviour of a simple 2D airfoil is in practice almost perfectly understood, any complicated CFD simulation or test apparatus is normally first proof tested on a 2D airfoil: if it fails this test then something is wrong and the model must be corrected. So, 2D airfoils are the basis, 2D is real.
Let's start then with the most simple theory that has been developed, the "thin airfoil theory”. Even it is based on the simplification of a bi-dimensional (aka wing of infinite span) inviscid and incompressible flow, it gives a surprisingly useful insight to the behaviour of an aerodynamic body since this theory allows to learn that: a) only the camber of the airfoil counts in the generation of lift and moment; b) the lift coefficient has the value $C_l = 2\pi\alpha$, where $\alpha$ is the angle of incidence; c) the coefficient of moment is constant in respect to the point lying one quarter of the chord behind the leading edge (quarter-chord point) and d) yes! in this case Bernoulli does work and it is used to calculate the just given equation for $C_l$ (but that’s another matter).

Airfoil nomenclature. Source: https://commons.wikimedia.org/wiki/User:Ariadacapo#/media/File:Chord_length_definition_(en).svg

Step 2: real 2D airfoil

Nice thing the “thin airfoil theory” but... what about the drag? “It seems to me that the theory, developed in all possible rigor, gives, at least in several cases, a strictly vanishing resistance, a singular paradox which I leave to future mathematicians to elucidate”, Jean le Rond d'Alembert. He was obviously right, so right that this contradiction is named after him.
Anyway, even without being committed mathematicians, the answer is simple: since the thin-airfoil theory neglects: a) the 3$^{rd}$ dimension; b) the compressibility and c) the viscosity of the fluid, then the culprit is one of these three.
So: a) cannot be since also 2D bodies generate drag; b) compressibility becomes important only for speed bigger than Mach 0.3 but drag exist also for very low-speed flows, thus it cannot be; then the winner is: c) the viscosity!

Boundary layer around a typical airfoil. Source: https://www.researchgate.net/publication/299486909_Design_of_Diver_Propulsion_Vehicle_Ganendra_RI-1_Using_SolidWorks_Flow_Simulation
Unfortunately viscosity makes the simple equations of the thin-airfoil theory no more solvable per hand and therefore either CFD simulations or, before computer age, extensive wind tunnel tests has (had) to be performed. In particular, wind tunnel tests allow(ed) to learn that viscosity generates a "boundary layer" which interacts with the flow, leading to: a) viscous drag; b) stall at high angle of attack; c) importance of the distribution of the thickness around the camber and d) more generally: non-linearity in all aerodynamic actions (lift, drag and moment - except maybe at small angles of attack). Wind tunnel tests provide(d) also a common basis of comparison among the various airfoil’s geometries: a paper like “Summary of airfoil data” by Abbott, Von Doenhoff and Stivers, published in the 1945, is still today a must-read.
And what about if we go faster? Then also compressibility becomes important with all that this entails, like the formation of the wave drag.

Step 3: ideal 3D

This one is actually "one step forward and two back". The step forward is obviously going from 2D to 3D i.e. from infinite to finite wing; the steps backward are the elimination of viscosity and compressibility, again to make the mathematical model easy enough to be solvable by hand. Indeed, the same mathematical instruments used for the thin-airfoil theory are now still valid except for one essential difference: in 2D, the wake is a line (in a mathematical sense i.e. it possesses no thickness) and doesn't contribute to the aerodynamic actions; however in 3D, as depicted in the following picture, all these wake lines shed from the trailing edge build a surface (called “vortex sheet”) which now does contribute to the generation of the aerodynamic forces:

Vortex sheet wing model. Source: https://www.researchgate.net/publication/344467888_Aerodynamics_and_Control_Aspects_of_Formation_Flight_for_Induced_Drag_Savings
Unfortunately the flow on each one of this line possesses a very "chaotic" velocity which, again, complicates too much the equations. Some other simplification was therefore needed to make the problem solvable again. The simplification found consists in considering a wing with a span much bigger than the chord, i.e. a wing with an high aspect ratio AR. Why that? When the AR is big enough, it exist an “optimal distance” behind the wing which is: a) far enough from the wing so that the flow has lost most of this "chaotic" behaviour (so called “far-field”); but b) not so far that the shape of the wake has become too much different from the starting shape it had by the trailing edge (so called “near-field”). The following picture nicely depicts these three region of near-field, far-field and intermediate (optimal distance) field:

A NACA0012 wing with the near, intermediate and far-field regions.
Source: https://www.researchgate.net/publication/322284435_A_parallel_stability_analysis_of_a_trailing_vortexA_wake
Within the intermediate field (the “optimal distance” we were looking for) a plane is chosen to do sums, which is called “Trefftz plane”:

The Trefftz plane lying within the “intermediate field”. Source: How do wing tip vortices that interact with the wing surface affect drag?
Why do we choose a plane just there? Because in the Trefftz plane the whole wake becomes just a thin line (in red in the picture) having the same shape of the trailing edge of the wing. So, if we do the math on the Trefftz plane, the whole messy wake can be substituted by a geometrically known thin line: that's a smart choice!
So, on the Trefftz plane the equations become again solvable by hand and allow to get some very useful results: a) moving along the wingspan, the wing can be seen as a sequence of 2D airfoil (as in Step 1 of this answer) each one generating its own portion of lift; this is called "spanwise lift distribution"; b) everywhere the lift is different between an airfoil and the adjacent one, a vortex is shed perpendicular to the trailing edge and contributes to the vortex sheet; c) well behind the wing (far-field), the vortex sheet rolls up into two big vortices that eventually dissipate due to the viscosity of the air; the dissipation could take some minutes and dictates an adequate separation between successive aircraft; d) the aerodynamic force now possesses both a lift and a drag; e) the drag reaches a minimum when the spanwise lift distribution is elliptical; in this case it exists a simple mathematical relation between lift and drag coefficients which is $C_{d_i} = C^2_l/\pi AR$; if the spanwise distribution of lift is not elliptical, this expression becomes $C_{d_i} = C^2_l/\pi ARe$ where $e$ < 1; f) yes, also in this case Bernoulli does work and it is used to get the previous equation.
The following picture nicely depicts the points a), b) and c):

The spanwise lift distribution causes the shedding of a vortex sheet behind the aircraft. Source: https://upload.wikimedia.org/wikipedia/commons/1/18/Aircraft_wing_lift_distribution_showing_trailing_vortices_%283%29.svg

Step 4: 3D real wing

So, do we still need today, in times of realistic CFD simulations, all this blabla on 2D airfoils and wing with big AR? Isn't it enough to launch a computer simulation to get all the information that we need? Well, yes but! if the induced drag needs to be evaluated then there's nothing else to do but define a Trefftz plane behind the wing and make calculation on it. Why that? Because this is how the induced drag is defined: you get a plane in the intermediate/optimal field and you do the math on it. The drag jumping out from this calculation is the induced drag.

That’s all!

Hopefully it was not too difficult to follow, comments are obviously welcome.

Bonus material, in no order whatsoever

A misunderstanding about the relation $C_{d_i} - C_l$:

when all the simplifications listed by “Step 3: ideal 3D” have been put into practice, the aerodynamic force can be finally calculated and decomposed in its two components lift and drag; when afterwards the lift is made equal to the drag, then the much (in)famous relation $C_{d_i} = C^2_l/\pi AR$ is obtained. This relation only implies that lift and drag have been generated by the same mathematical (and physical) process, nothing more, nothing less; it definitely does not imply that it exists a lift-generated or a lift-induced drag; actually that relation could (should?) be written $C_l = \sqrt{C_{d_i}\pi AR}$: would that imply the existence of a "drag-generated" lift? Obviously not, otherwise the paradox would be created that having a lot of drag is unavoidable to have a lot of lift.

A second misunderstanding about the relation $C_{d_i} - C_l$:

On closer inspection it is clear that the relation actually involves coefficients: that implies that more lift (lift, not coefficient of lift) might actually "induce" less drag.

A general misunderstanding about “lift-generates-drag”:

To realise that the association “lift-generates-drag” is in general not correct, it is enough to consider a 2D airfoil (as in Step 2): it generates plenty of lift without any lift-related drag (only viscosity- and compressibility-related drag)

An important takeaway:

From “Step 3: ideal 3D” it should be now finally clear what induced drag truly is: it is a kind of aerodynamic drag which appears when the simplification of infinite wing is dropped. That’s all. It has nothing to do with the amount of lift generated, only with the fact that the wing somewhere ends and the lift becomes null there. It could actually even be said that the induced drag is not the drag due to lift but the drag due to the lack of lift!

On the naming “induced” drag:

The naming is misleading because it suggests the controversial definition of “drag due to lift”. Actually, as we have seen in “Step 3: ideal 3D”, there is indeed an "inducing" phenomenon involved in the process: the spanwise lift distribution inducing the vortices in the vortex sheet. This is where the name comes from! So, the definition might become correct if expanded into: “drag due to the spanwise variation of lift” (which, again, is a consequence of the fact that the wing somewhere ends and the lift becomes null there)

Again on the relation between lift and drag:

An aerodynamic body moving in a flow generates an aerodynamic force, period. The decomposition of this aerodynamic force in lift and drag is just a pure convention. A totally different convention is used for example in the helicopter world where the aerodynamic force is decomposed in a component parallel to the rotor shaft, positive upward and one perpendicular to it, positive against the sense of rotation. The sum of the former gives the thrust produced by the rotor while the sum of the latter gives the torque that the engine has to generate to keep the rotor spinning. So, no lift nor drag in helicopters. Now, that a relation between these two terms (lift/drag or thrust/torque) always exists is just because they are the two sides of the exact same coin. They must be related because they both pop up from exactly the same phenomenon: you have an aerodynamic force and you split it in two parts... these two parts are obviously related since they both arise from the same thing.

On the "tip vortices" model

This model is, among the plethora of explanations, the less wrong. Anyway, as already seen, tip vortices form backward but they are so far from the wing (in the far-field) that they cannot influence the wing anymore (but they do influence another airplane flying into them). The right picture for this model would be therefore the following one, which better depicts the vortex sheet:

A more correct representation of the "tip" vortices. Source: https://cdn-images-1.medium.com/max/1600/0\*2gL-QOXqx51qNdAE.jpg

On the "momentum" aka "energy" aka "pushing air down" model

Even if the physics behind this model might be correct, I personally find this model way too generic: you take some random quantity of air, you randomly push the air down, you associate this pushing down to lift, but also to drag, you mix everything and you get $D = {blabla} L^2$. And in some versions of this model that's not the end of the story: since in the (in)famous relation a $\pi$ and the aspect ratio AR make their appearance, the random quantity of air is made "less random" using a tube of air with the same diameter of the wing: choosing a tube of air as big as the wing, we get in one shot the aspect ratio AR and the $\pi$ in the equation. But then, why a tube exactly? What if we had chosen a parallelepiped instead? Isn't a parallelepiped better? Maybe with a width a bit bigger of the wingspan to get also some tip vortex? And why not a tube which invest the wing from above? You also get the $\pi$ and the AR. Or even better: why not a downward angled tube? Seen from the front it looks like an oval i.e.an ellipsoid and this could be related to the fact that an elliptical lift distribution is the one giving the lowest induced drag... bang! we've got $\pi$, AR and elliptical lift distribution: three birds with one stone. Whatever. Furthermore, the obtained equation relates $D$ with $L^2$ which is wrong since the actual relation is between ${C^2}_l$ and $C_{d_i}$.

On the "lift is tilted backward" model

As said, the aerodynamic force is customarily split in 1) a component parallel to the airflow, called drag and 2) a component perpendicular to the airflow, called lift. As also said, this is just an arbitrary and convenient choice that, for example, is definitely not useful for rotors analysis where it is preferred to split the aerodynamic force in respect to the orientation of the rotor's shaft. So, what does it actually mean that the lift is tilted backward? It simply means that... well it is not lift what we are looking at! Lift cannot be tilted backward, per definition: lift is perpendicular to the flow, that's it! If it's not perpendicular to the flow then it is not lift. A better explanation would be to say that, due to the downwash, the wing sees an airflow which is now the composition of $V_{flight}$ (mainly horizontal) and $V_{induced}$ (mainly vertical) and therefore this composed velocity has a lower $\alpha$ in respect to the wing. Therefore the aerodynamic force (and not the lift) is more backward tilted and its decomposition gives, in turn, more drag and less lift. This representation, albeit simple and effective, is anyway not really correct because it implies that the downwash in the wake acts on the wing. But the wake is not  on the wing rather behind it, so this model supposes that what happens in the downstream (wake) influences what lies in the upstream (wing), which is also not totally correct.

"The effect of this vortex is to locally decrease the angle of incidence therefore reducing the total lift generated by the wing. To compensate for this reduction, the angle of incidence has to be further increased with a related increase of drag.": This does not explain why drag is more for the finite wing at the same angle of attack.

https://www.perfectedflight.com/the-truth-about-induced-drag/

@PranavHosangadi this is not the topic of this question/answer. The topic is mainly to explain that induced drag is a strictly 3D phenomenon and to give a qualitative explanation of its source. I've seen many times that the concept of induced drag is associated with 2D airfoils and lift, which are both not correct

@sophit the point on the drag velocity curve is the minimum total drag or minimum thrust required. The point of minimum power corresponds to ${{\sqrt{C_l}/C_d}}_{max}$.

@Jim, that website is a great example of poor inductive reasoning. The underlying issue is a conflating of aerodynamic reaction force with lift. To have a list of 4 statements about induce drag, which are all true, and then effectively say "which one is it, they can't all be true" is logically outrageous, and is the reason why this garbage was published: https://www.scientificamerican.com/article/no-one-can-explain-why-planes-stay-in-the-air/

My takeaway was that pilots are taught one definition and engineers another.  That seems to the crux of the confusion. As both a pilot and an aerospace engineer I have seen both first hand.

@AerospaceDoctor: thanks for the correction and for the link at the scientificamerican's article, I didn't know about it... that is a really nice collection of dozens of misunderstandings

@Jim: then you have the power to correct the wrong use when you hear it  Also because according to the wrong definition, the induced drag is the drag due to the generation of lift, implying more drag with more lift but this is wrong as visible in the last picture (plotted at constant lift)

So the super short answer is, induced drag is energy lost from "leakage" inherent in having a wing that terminates at the tip.

@JohnK: thanks for your comment, I'll incorporate it in the revised answer that I'm preparing

@sophit, I don't mean to quibble, but exactly what is the point of the 2D vs 3D comparison? There is nothing in nature that is 2D.   2D artifacts are mathematical simplifications, abstractions, that only exist in our minds.

Anyway the 2D analysis was/has been very helpful in defining the basic aerodynamic behaviour of an aerodynamic body, like the importance of camber, the need of a pointing trailing edge, the boundary layer theory and so on. Furthermore, until the development of powerful enough computers, 2D was the only doable thing

@sophit "drag due to the spanwise variation of lift" What dooes it mean ,if lift is constant  over spanwise, then induce drag dont exist?

@JurgenM: again, lift always does change spanwise because at a certain point the wing ends and there the lift suddenly goes to zero (from whatever value it had on the tip of the wing). So induced drag always exist (on a not infinite wing) and its value depends on how the lift is distributed spanwise. The minimum is for an elliptical spanwise lift distribution.

@sophit But why induced drag depend on lift spanswise distribution,so section with higher Cl(close to root) induce more vertical flow se here is induce drag higher?

The equation for the induced drag pops out from an integration of the lift from tip to tip and it can be demonstrated that it has a minimum for an elliptical spanwise lift distribution. So it's not really the local value of lift that matters but its variation.

@JurgenM: I just wrote the opposite actually: "which is also not totally correct". Btw I'm going to use your picture here to expand this answer of mine: where did you find it?

@JurgenM This sentence "is anyway not really correct because it implies that the downwash in the wake acts on the wing" does not contradicts the next one which is anyway the correct explanation of the phenomenon: the "downwash" related to the induced drag actually begins in front of the wing. Plus with my first sentence I was debunking the wrong explanation about induced drag, while with the second one I was giving you the correct explanation: sorry but comparing the 2 sentences is therefore wrong from you side... and please remove the character in bold...

@sophit This was absolutely incredible. You just summarized an entire aerodynamics course in one reply. Kudos to you sir.

@interested22:  thanks

Let's present a simplified engineering point of view based on momentum and energy.
Lift is caused by imparting downward momentum $mv$ to the incoming air stream $\dot{m}$:
$$L=\dot{m}v$$
The power required to impart this momentum is related to the kinetic energy:
$$P=\frac{1}{2}\dot{m}v^2$$
This power requirement manifests itself in the form of induced drag,
$$D=\dfrac{P}{\mathrm{TAS}}$$
Written altogether, we get
$$D=\frac{L^2}{2\ \dot{m}\ \mathrm{TAS}}$$
That equation shows that purely from the point of momentum and energy one must also have lift induced drag. As we know, induced drag is less when flying faster (higher $\mathrm{TAS}$ and $\dot{m}$) and when wingspan increases (more air affected: higher $\dot{m}$)

Comments are not for extended discussion; this conversation has been moved to chat.

Because there is no universal definition. The term is used in many, multiple contexts, for different purposes, and has a different meaning in each context it is used in.  And these different meanings are inconsistent with one another.  The key to the confusion is the use of the word induced which implies that it is caused by some other phenomenon, generally assumed to be Lift.  This however, is not true.  The use of the term Induced Drag is an arbitrary separation of total drag into two pieces, the part which changes as AOA changes  (i.e., it increases as AOA increases), and the part that changes as airspeed changes, (also called Form drag). Generally, Lift is the component of the total aerodynamic force on the airframe that lies normal (perpendicular), to the flight path and drag is the component of the total aerodynamic force on the airframe that lies parallel to the flight path. Form drag is the drag that would exist if there were no Lift, (just from the airframe moving through the Air). So Induced Drag is whatever additional drag above the amount of Form Drag, that exists when there is Lift. (But it is not caused by the Lift),
Graphically, if you imagine the total aerodynamic force as a vector attached to the aerodynamic center of the airframe, because the airframe is moving through the air mass, this vector MUST be titled aft from the direction normal to or perpendicular to the local airmass relative velocity vector. Lift is the component of this vector force that is perpendicular to the velocity, and Drag is the component that is parallel with it. Thinking of it this way, it is obvious that as AOA increases, the vector must tilt further and further aft, and the drag component will grow larger and larger.
But this drag component is just that, an arbitrary mathematical tool used to break up what is the aggregate sum of all aerodynamic forces into pieces that we can talk about discreetly. And it itself is not just Induced Drag The drag component itself contains Both Form Drag and Induced drag. We have to continue with our virtual mathematical analytical knife and slice it into two further pieces, Form Drag, and Induced drag, before we have isolated this creature to use it for analysis or discussion.

I agree with you, that's why I wrote that mine is not the answer but just an explanation why a sentence like the following are wrong: "induced drag is the drag generated by the lift" or "induced drag exist also for airfoils" or "induced drag is just a tiny amount of the total drag"

@sophit, Yes. We agree. Sorry If my post implied otherwise. Here, I'm attempting to explain why there is such confusion about this...

The root of the confusion is we haven't wanted to burden pilots with the underlying physics, so they lack the intuition about what's behind the curtain.  At the most simplistic level, engineers distill this all down to stall speeds and maneuver speeds, and for most pilots, this seems good enough.  But if you start flying with an AOA indicator, it just opens up a whole new world that contradicts some of what you knew.  Become a fighter pilot and suddenly wing loading becomes a very real thing, not a white-board BFR topic.  If you're a helicopter pilot you care a lot about unloading your rotor.

@Max, Yes, unfortunately, this sentiment is not just misplaced and unnecessary, it is dangerous. It's unnecessary because the physics and math to explain the aerodynamics is not quantum mechanics and tensor calculus, at best it involves simple algebra. Dangerous because it creates what are WRONG-HEADED assumptions about what is going on that lead to bad decisions that can, (and have), resulted in fatal consequences.  Also, add my enthusiastic support for AOA education! ... and it simplifies these issues!

You could say it's not induced by lift, but induced by AoA.

@TomMcW,  Well, yes, metaphorically, I could agree, except that would reinforce the point I am trying to dispute, i.e., that Induced Drag (because of the implication of causation implied by the word "Induced",  is not a real thing, it is just an arbitrary mathematical construct we have created to try to help explain things in certain contexts.

The concept of causation requires something real to be the cause, and something else real to be the effect. Neither Lift, nor Induced Drag are real things. They are like momentum, pressure, or frequency. These are just mathematical constructs. It is silly to apply the concept of causation to anything that only exists as a tool in our mental or mathematical thought processes.

@CharlesBretana: I really like these last comments of your

@sophit,Thanks for the compliment! I know my approach to this can often be seen as overly pedantic and philosophical, so it's nice when someone notices (and appreciates!), the underlying issues involved.

@CharlesBretana: if it's right, it's right even if it's pedantic and philosophical. And if it's wrong it's wrong, even if it's short and appealing

You two are on a whole different level than I am, and I am actually very aware and sensitive to reversing cause and effect relationships, but where do we draw the line when there is a 100% irrefutable correlation between two things?  (Does increasing lift "cause" an increase in induced drag, or are you really causing induced drag and extra lift is a beneficial side effect?  Or are you causing both, and they just happen to always both occur?)  It is important to know that when you increase AoA and lift you also increase drag, but practically how is safety affected if "cause" is confused?

You draw the line at confusing correlation with causation. The Semantic definition of these words is not complicated. The ymean totally different things. There's agreat book about this entitled "How Not to be Wrong - The power of mathematical thinking.:"  https://www.amazon.com/How-Not-Be-Wrong-Mathematical-ebook/dp/B00G3L6JQ4/ref=sr_1_1?crid=3E200OTB6YPVG&keywords=How+Not+to+be+Wrong+-+The+power+of+mathematical+thinking&qid=1662415586&sprefix=how+not+to+be+wrong+-+the+power+of+mathematical+thinking%2Caps%2C109&sr=8-1

The issue with confusing them, is that when two things are correlated, but one is not the cause of the other, thinking that they are causally related can easily lead one to attempt to change the causee by changing the causor. Body temperature and sickness are correlated, but does temperature cause sickness? We used to universally think so. We used to attempt to bring down fever when someone was sick, inadvertently interfering in the bodies' attempts to fight  (with higher temperature), the real cause of the sickness, - the infection.

I get what you are saying and agree to a point, but I question the usefulness of such a sharp distinction in most practical applications.  Picture the following exchange - Instructor:  "As you increase AoA to maintain altitude as you slow down what must you remember?"  Student: "IDK, what do you mean?"  Instructor: "Your drag increases as you increase lift so you need to add power."  Student:  "First, slowing down and increasing lift doesn't CAUSE additional drag, and second I don't even need to add power if it did because drag is not real - it is just a mathematical construct."

I agree with you.  In practice, only a small minority of correlated parameters are misconstrued as being causal, can actually result in wrong conclusions or dangerous assumptions. But when they do... I quibble about this (specifically the Lift causes drag meme), because it implies, (and creates) a WRONG idea about what Lift and Drag are, that is only true when examining a very special case, that is, the Lift and drag produced only by the wing, (excluding all other aerodynamic forces on the airframe), in 1G level flight, to wit,

that they are separate, real, independent forces acting on the aircraft, that actually act only through a single point. I know, it's obvious to you and I that this is a simplification that is 100% accurate in predictive  capacity, and allows us incredibly useful mathematical analytical tools to calculate aircraft performance and behavior, but it does not require an Einstein to teach, and/or understand the true nature of these aerodynamic forces as well.

Another glaring example is the meme about wind. So many pilots I talk to still think that the wind is "Pushing" on the  aircraft. They think the ground speed in a headwind is reduced because the headwind is exerting a force on the front of the aircraft impeding it's forward velocity. They believe a crosswind "pushes" the aircraft sideways.  This exemplifies the difference between common sense  and the true  understanding of things.  I've heard a pilot say that if you turn 180 degrees in a strong headwind, you will have a tailwind, your airspeed will decrease,  and so you might stall.


text:
How many mid-ocean battery swaps are needed for an electric A380 to refly the first transatlantic flight?
Context
To understand what the current level of electric airplane propulsion is with respect to large passenger airliners I developed the following question:
Question
How many battery swaps would be required to fly the same route as the first non-stop transatlantic flight with an electric equivalent of a passenger aircraft able to transport +-600 passengers at once with a cruise speed of Mach 0.85?
Assumptions
To minimize the ambiguities regarding the question I made the following assumptions:

The first non-stop transatlantic flight took place from Lester's Field, near St. Johns, Newfoundland on June 14,1919, and landed June 15,1919, at Clifden in Ireland. The time for the crossing was sixteen hours, twenty-seven minutes.
It is assumed there is currently no battery technology that is able to perform the flight for 600 passengers without reloading during the flight, a mid-flight battery swap system is assumed.
The battery swaps are assumed to be possible at 34.000 feat altitude at mach 0.85.
The battery is assumed to be fully charged upon placement in the aircraft.
A suitable runway can be built/is available at/near the departure and arrival destinations.
Max thrusts required for take off and landing are ignored based on assistant launcher aircraft/rialguns. I.e. the aircraft is only considered in (optimal) cruise conditions.
The batteries can be located, in fully charged state on any position on the surface of the globe along the route.
Current (2020-06-30) battery technology is assumed. In particular the specs for the Pipistrel Velis Electro with 11.0 kWh, capable of delivering a constant 49 kW is assumed.
A lithium battery density of 500 W/kg and 900 W/l is assumed. (Optimistic assumption of portability of technology that is not been proven in aviation applications despite cyclic acceleration loading, vibrational loading, temperature loading).
The equivalent electric engines are assumed to be required to produce the same thrust in newtons as their combustion equivalent engines at 4x348=1392 kN.
Speed of sound at cruising altitude of 34.000 ft of 240 m/s is assumed.
A constant power usage of 1392.000x0.85x240=283968000W=283968 kW =~ 284 MW is assumed required to be continuously delivered by the electric jets.
The mass penalty of the battery swap system is assumed 5000 kg. (Random unfounded optimistic estimate)
The mass penalty is electric jet-engines is assumed to be twice the mass of the A380 Trent 970-84/970B-84 engine of 6246 kg is used, resulting in a mass penalty of 4x6246= 24.984 =~ 25000 kg.
An additional mass penalty of 10.000 kg is assumed due to requirement of aircraft reconfiguration requirements. E.g. concerning electric cabling, lack of aircraft design optimization experience with large replaceable batteries in stead of wing-integrated fuel tanks. (Random optimisitic estimate/guess)
The flight should be reproducible at least 95 % of the days of the past decade, to prevent estimating on unlikely favorable weather conditions.

Notes
Different assumptions can be made, please use comments to argue why assumptions could/should be adjusted, and keep answers for explaining how one can come up with the estimated amount of required battery swaps.

It's really not this complicated. You need about 50 because electric motor is about 2x more efficient (near 100% vs around 50%) than a turbine and battery is about 100x less energy dense (0.4MJ/kg vs 40MJ/kg) than jet fuel.

500Wh/kg is kind of overly optimistic as your linked source it's typically 90Wh/kg.

@user3528438 thank you, I have updated the reference (to the reference used in the claim for the 500 W/kg in the article). Your approach provides a nice sanity check, which also appears to indicate I made either a computation mistake or too conservative assumptions.

This question does not make any sense at all.  If you want to recreate the first transAtlantic flight, you do not use a 600 passenger airliner travelling at Mach 0.85.  (If indeed you could even get a 600 passenger electric plane to that speed.)  You use something equivalent to the twin-engine biplane used by Alcock & Brown: tps://www.history.com/news/first-transatlantic-flight-nonstop-alcock-brown

With so many assumptions and handwaving I feel this question has no real value or broad appeal.

So there's going to be some sort of mid-air swap-out of batteries?

@jamesqf Thank you, indeed assumed a too loose definition whilst using the word "recreate". I adapted the question accordingly by replacing "recrate" with "re-fly" to accommodate the difference in flight parameters between the original flight and the proposed flying route.

@GdD Thank you, I implicitly assumed the battery swap system in formulating the question, I made the assumption explicit and included the assumption that the battery swaps are possible in cruise and deliver fully charged batteries.

Kudos for putting a lot of thought into this question, but unless you can come up with a semi-plausible method for addressing #3 then the entire premise crumbles and isn’t worth spending any effort pondering.

@MichaelHall much appreciated, I think design and feasibility analysis of the hypothetical battery swap system is beyond the scope of the question. Thinking about things that might not directly appear feasible are not necessarily a waste of time. I think this question can contribute to developing a very basic insight into the logistical challenges faced in electric flights that use battery swaps on such a large scale.

Assumptions

The total mass penalty is assumed of 5000+25000+10000=40.000 kg is assumed w.r.t. a conventional A380. This is assumed to go at the cost of fuel tank/battery costs.
The A380 has 253,983 kg fuel capacity, leaving 213.983 kg of battery capacity.
The distance of the journey is 3040 km.
The A380 cruises at 903 km/h.

Computations
With a power density of 0.5 kWh/kg, a total capacity of: $213983\cdot 0.5=106991.5 kWh=106.991MWh$. Since the engines require a continuous flow of 284 mWh, the complete battery set would have to be swapped every $\frac{284}{107}=2.65..$ times per hour, which is approximately every 1356 seconds. Since the transatlantic flight covers 3040 km at a velocity of 903 km/h, the flight takes $\frac{3040}{903}=3.37$ hrs. Therefore, according to the set of assumptions, $\frac{3.37\cdot 3600}{1356.22..}$ = 8.94..=~9 battery swaps would be required, with a station approximately every 337 kilometers.
Doubts
The assumptions made in the question appear to be highly inaccurate, hence a more detailed analysis of the assumptions, in partciular to the battery swap system mass and scalability of the battery, engine and thermal systems could perhaps illustrate the (lack of-) accuracy of the estimate.

213983⋅0.5=106991.5Wh=106.991kWh= 0.107mWh . the second term should be kWh, thrid MWh (M not m), forth GWh. so your answer is off by 1000 times.

I confirm the mistake in the math.

@user3528438 Thank you, I corrected the mistake by switching the units from Wh to kWh and propagating the impact of the correction through out the remainder of the estimate.

Power is in MW (megawatt), not mWh (milliwatt hours). Also you completely neglect that MLW is much smaller than MTOW so unless you ditch the batteries before landing you're in trouble.

@Sanchises Thank you, I corrected the units for power in the question from mW to MW. Yes, those neglections are implicit to the assumptions stated in point 5 and 6, pertaining to assuming a suitable runway can be built, and that the aircraft is only considered in cruise condition.

source: Stack Exchange

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text:
Where are the fuel tanks located in an Antonov An-225?
Does anyone have answer for where the fuel tanks are located on the Antonov An-225?
(photo attached for explanation if anyone could)
Would love to know how many tanks are on the aircraft and how the system works.
*Please let me know if I've colored right sections on the wings indicating the fuel tanks positions.. if not, let me know which ones to modify.
Really appreciate your help!

The 225 is derived from the An-124, which has 10 integral fuel tanks in the wings. Comparing the specs, it looks like fuel capacity is the same as the An-124, so the center section of the wing (the only new part of the wing) doesn't contain fuel.
Based on that, I think the tanks are in sections 2-6 and 13-17. I'm assuming the outer wing sections 1 and 18 are not used as tanks. If those were used as tanks you'd have higher loads on the wing during roll maneuvers.

The tanks near the wingtips might be Surge tanks and not normal fuel tanks. They're found on many transport category aircraft, they're there to provide space for fuel flow during refuelling in case of overfilling and for fuel to collect during the violent manoeuvres

One would hope that transport category aircraft don't experience too many "violent maneuvers", @AmanVishwakarma!

Haha I know, there are baffle check valves incorporated, but you can never be too safe, right? It's just a fail safe design feature

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text:
Why does power help us maintain altitude in slow flight?
I was asked this question and didn’t know how to phrase a nice and easy explanation.
What I said is- well because drag is now increasing Un- proportionally to lift, we need something to generate more lift, and since pitching up like we would do in normal speeds isn’t an option because it would just increase drag more, our only way to create more lift is increase thrust- and in so increase that vertical component of thrust that acts as lift and help us maintain altitude.
Am I right in explaining it like that? And is there a nicer and simpler way to explain that?
Something with the 4 forces and thrust-drag and lift-weight couples?
Thanks!

The vertical component of the thrust line is a significant factor. Easiest way to visualize it is to take it to the extreme; an
airplane with so much power it's able to hover on its propeller while pointing straight up.
Drop that back down to a deck angle of just under 15 degrees, and a simple vector calculation shows that an engine making 600 lbs of thrust has a vertical component of about 150 lbs, which is effectively adding to wing lift.
Take away the vertical thrust component helping the wings, say by having an engine mount that tilts down to put the thrust axis back to horizontal, and it's as if a 150lb passenger suddenly appeared in the seat beside you.  It's not a lot, less than 10% of the total lift say, but it's not nothing either.
Add in extra lift from slipstream effects, and that's probably the major component of it all, in terms oh how power influences sink rate in slow flight.
On large turboprops that have huge propeller discs that may cover 1/3rd of the total wing span, slipstream effects are dominant with flaps down, and in the approach configuration, sink rate is directly and immediately affected by power changes.

It is not correct to say that power controls altitude. In slow flight, it is taught that power controls altitude and pitch controls speed. Yes, it works, but you have to always keep in mind that a power change will always require a pitch change and a pitch change will require a power change, if you want to maintain the same trimmed speed, altitude and angle of attack.
As you might very well know, in a slow flight, you reduce your power first and start putting down the flaps to sort of keep the aircraft in an approach configuration. Then you pull back on the stick until you are close to the stall speed. Once the speed you want is reached, you add power as required to maintain speed and altitude. If you lose altitude, a little addition of power will arrest it. But trust me, this will also increase the speed by small margin. This might not be registered in the air speed indicator of a smaller aircraft. Similarly, an increase in pitch in attempt to reduce an increasing speed, will change the altitude. So, it is not fixed. Pitch and power are not two separate entities. They always work together. Try flying a high performance aircraft with powerful engines and with a load of inertia and you will see how true my words are.
The reason why more and more power is necessary to successfully accomplish a slow flight is because you are operating below the L/D speed of the aircraft. Once you are below this speed, the increase in induced drag (due to high angle of attack) increases the total drag on the air frame. To overcome this drag you are required to add power or energy. We call this operating behind the power curve or the region of reverse command. Reverse because normally, you need an increase in power to fly at a higher speed. But behind the curve, to fly at a lower speed, you need more and more power.
Look at the graph below, the GD (Green dot) speed is the L/D speed. As you can see, as you go below the L/D there is a steep increase in drag.

I think it fair to say that power does control altitude; obviously there are other factors, but an increase in altitude requires an increase in potential energy, which is provided by the engine.  In contrast, lifting the nose up will generally not result in an altitude gain, certainly if the aircraft is in slow flight already.

Total Aircraft Drag is the sum of Induced Drag and Parasite Drag. Induced Drag reduces with (the square of) speed whereas Parasite Drag increases with (square of) speed. If we plot this we get a somewhat U shaped curve for Total Drag at different speeds.

If we draw a horizontal line representing a particular Drag value - Except for the lowest point on the curve, representing the least Drag point, every other point above lowest Drag on the Drag axis of this curve corresponds to 2 points on the curve, ie corresponds to two speeds. Since Power is proportionate to Drag, every Power setting corresponds to 2 speeds except at the lowest point on the Drag curve.
So, as speed increases in flight, the airplane could accelerate to, and maintain the first/slower speed, or further accelerate using available Power till it reaches the second/higher speed value.
Typically we would not want to fly at the lower of the speeds when the same power can give us a higher speed.
"Why does power help us maintain altitude in slow flight?" - actually, the forces and force couples at play are the same whether high speed or low, but from the the dynamic stability point of view, low speed and high speed differ as follows - lower speed lies in the zone of dynamic instability in speed, ie any drop in speed results higher Drag thus tending to naturally reduce the speed further unless Power is added to the equation. If power cannot be added, the only option is to push the nose down and trade altitude for speed (provided ground contact is not a factor!). Due to the shape of the curve, any hesitancy in taking the counter-action would result in a rapid speed loss requiring more and more power. This is commonly referred to by pilots as "the wrong side of the drag curve". Compare this to the right side/higher speed zone, where a drop in speed would result in lower Drag thus naturally tending to return the airplane to the desired speed without much by way of a Power input.
Similarly, for completeness of understanding, you may like to figure out in your mind, the dynamics of what happens when there's a slight increase in speed.

a nice and easy explanation ...

Aerodynamics  ...  Cessna 172  ... Slow flight
Things are generally safer when nice and easy so ...
For this type of aircraft, Center of Gravity is checked as part of the pre-flight.  If CG is in range, your plane should be "staticly stable", and trimmed for speed. Confirm this with your instructor.
Now, because your CG is in the right spot and you know how your plane works, the nice and easy explanation is:
If my plane is trimmed for a given speed (65 knots for example), adding or subtracting power will make it climb or descend at approximately the same speed.  If you have no power, your plane will glide at 65 knots.  Adding power lets you control your glide slope at the same speed.  Adding more power lets you climb.
Not all planes are set up like this.  It is very important to get information specific to your 172, and to talk about it with your instructor.

Yes thats true, but when we are cruising 90 kts, and want to climb from 2900 to 3000 feet, we don’t add power, even though it will indeed make us climb, we would just pitch up...           So not sure “airplane wants to fly trimmed airspeed” is the best explanation for this.

@leha007 "2900 to 3000 feet" is a minor adjustment, in a landing pattern, slow, it is much safer to control altitude with throttle.  Look at the graphs below, what might happen if you pitch up 200 feet AGL and start slowing down more?  Not worth the risk.

It is very important to know that your "energy state" is V$^2$, at 90 knots you have plenty of it, at 65 knots not as much.  Adding throttle (thrust) takes time to build speed (pitching down greatly helps), but if you get "caught short" low and slow you have neither the time or the altitude to recover.  An unenexpected downdraft once had me skimming across the corn tops 1/4 mile short of the runway (I added power before climbing a bit).


text:
Why is there a a nose-up pitching tendency during a forward slip in a Cessna 172?
Why is there a tendency for the nose to pitch-up during a forward slip in a Cessna 172 (According to the TC Flight training manual)?
Quote:
"If full rudder is used, considerable aileron pressure may be needed to maintain the bank. There will also be a tendency for the nose to pitch up as a result of the banked attitude and rudder input"

I'd suggesting including in the actual question the specific aircraft where you have noticed this.  PS t-tailed aircraft often pitch nose-down in a slip.  Might be related.

Can't say I've ever noticed that myself, but I'd be interested to see what that manual says.

It sounds like the manual is saying when you are banked, a yawing tendency is also a tendency for the nose to rise higher above the horizon.  I suspect that there may be more to the real story though, i.e. there may be some tendency for the aircraft to actually rotate about the pitch axis.

Never noticed that in my Cardinal. Altho I have done it so often I may not notice it and just push the nose down a little as put in full rudder and opposite aileron to lose altitude quick while on final. The plane straightens right up when controls are released.

What is a “TC Flight training manual”?

Mike Sowson if you don’t know that I can’t really see any reasonable or understandable reason for you commenting on this post.

I think what is a "TC Flight training manual" is a good comment.  Why doesn't it say Cessna 172 on it?  Pushing into a forward slip greatly increases drag.  The result is the plane slows and the nose drops.  I would strongly recommend actually doing a few with an instructor.  The 172 is ingeniously designed plane that handles beautifully in forward slips.  At 65 knots, trimmed, very little pitching was noticed (even with flaps), and plenty of opposite aileron was available.

It is because of opposite rudder in the bank.  In the forward slip and due to angle of bank the rudder input will push the tail down somewhat resulting in the nose coming up as it rotates around the normal axis which is now inclined due to the bank.  This is easier to see looking at a model plane.

Remember to think relative to the plane, not the ground.  Rudder input yaws the plane, it does not change AoA.  Pitching oscillations may occur due to drag turbulence acting on the horizontal stabilizer.  They are more noticeable with flaps extended.


text:
How can Ural Airlines fly an A320 from an unpaved field after an emergency landing?
Ural Airlines flight 1383 had to land in a field due to hydraulic problems and fuel shortage. The airline does not scrap it, but is repairing (source) and is going to fly it. A320 landing gear is not suitable for soft surface. How are they going to make it run and take off?

"The airline does not dismantle it, but repairs and is going to fly it." - what's your source for that? The article you linked says that "given the location of the aircraft it is likely to be dismantled in place".

@Bergi: added source link in the post.

It also helps that they are presumably going to run at minimum weight / fuel.

TLDR: cold winter will freeze the ground and make it hard enough.
First, there was a similar case of Alrosa flight 514 that landed on a disused runway in Izhma in September 2010, was fixed and flew to the closest airport in January 2011. So fixing a plane out of airport is nothing special.
The difference is that in Izhma that was a disused airport, and a local ex-employee had been cutting newly growing trees on the runway (summary), whereas Ural's A320 is sitting in a completely unpaved field.
But I'm from Novosibirsk and lived there for 30+ years, so I know how things work in that climate pretty well.
1. The ground freezes deep
By late January, the ground becomes frozen 1-2 m deep. That's why pipelines like sewer must be buried 2m deep in the region. Frozen ground is so hard that you can't dig it with a normal spade. To give a perspective: according to material stiffness tables, pure ice at -20°C is harder than pavement brick.
So, if the ground is even enough, there's no problem supporting one plane for one take-off run.
How do you make even ground?
2. There are winter ice roads in this climate
Winter ice road is built for winter months after temperatures become permanently below 0°C. You pour water to melt snow and the ground, even the surface, e.g. with a buldozer, let it freeze deep, and the road is ready. Climate in Novosibirsk isn't particularly cold -- there are much colder places in Siberia -- but every winter there's an ice road made over the water reservoir here.

Tempreratures near Novosibirsk are (almost) permanently below 0 from mid November till mid March. In January, weather is ideal: by this time, there's half a meter of snow on the field, enough to even the ground; anti-cyclones keep skies clear and temperatures low, around -20°C (which actually gives engines a boost in thrust).
Watering the field will actually make it freeze deeper, because ice is a good heat conductor, whilst snow is an insulator.
3. Isn't it dangerously slippery?
No, smooth slippery ice is actually very hard to make. People in warm climate think anything at < 0°C is slippery, but it's not. When I was 10-12 yo, I tried making a slide on a slope and failed utterly: I took a bucket of water and poured it on the ground, and the resulting surface was very bumpy like a sponge, you could almost walk uphill on it. Instead, to make a good icy slide, you need to smooth the surface beforehand and then carefully spray water, not letting it melt through.
Remark: cities in warm climate near the seas regularly have ice rain phoenomenon, when the air above the ground is below 0, but clouds masses are warmer and it rains rather than snows. I've never seen this in the middle of continent.
Only twice in my whole life there was a case when it rained in November same day as temperatures would drop below 0 permanently. Lots of stuff got covered with ice for months, and lots of sidewalks and paths in forests were like ice rink -- the first time, I was a schoolkid and we loved it! (BTW, salt won't help if there's lot of snow and temperatures far below 0.)
By the way, this ice wasn't forever, because it got gradually covered with snow. And normal snow isn't slippery at all, at least if it's colder than 0.
Icy surfaces in Siberia are very likely not in autumn, but in spring, when snow melts on the surface during the day and freezes at night.
So, ice isn't a concern at all. Plus, I believe they landed in this very long field (which seems to have no high-voltage line), so there's plenty of space for a stop in case of aborted take-off.
4. Won't it Damage the Field?
The field gets plowed every year, so bulldozing won't harm anything. Watering it will only do good, because the primary concern in this climate is to have enough moisture in the ground in spring. Dry winter with little snow is very damaging for agriculture.
So, How's the Plane Going to Fly Out?
The recipe, that I believe, Ural Airlines will follow, is this:

Put the plane on hard surfaces, like wood or metal sheets.
Even the necessary field.
Water it regularly.
Let the snow stay couple of weeks before the take-off, to make smooth and non-slippery surface. Compact it with heavy vehicles.
Wait a day with clear sky, and fly the plane, like Alrosa did.

ADDED: replying to @U_flow's comment regarding costs and labor.
First, I don't know if the surface has big waves that may make the aircraft jump before flying. From the photos it looks smooth, and they may need only to run a tractor to finely grind the dirt. But if the landscape is bumpy, they'll need a scraper. (Elevation map shows there are bumps, but smaller than 5 m.)
Here's an aerial photo:

the aircraft under inpection, photo by Ural Airlines
Second, ice roads are made anew every year, without much noise -- which probably means they cost a tiny fraction of a normal road. The real question is where you get water for the trucks, when they're not on a lake, but in a field. They might need to run trucks to the Ubinskoye town in 10 km. (A temporary pipeline seems problematic, because if water stays still, it freezes and ruptures pipes -- so operations must be very cautious.) Or they can bore a new well -- ground water in that region is high -- although, the place itself is on 10m higher ground.

But once the dirt is frozen and sustains a truck, the rest must be easy. Snowfalls are frequent but drop just ~5cm of snow every couple of days, so a truck can work just couple of times a week. Here's an example of one:

A random photo of such a truck, source

source title: "a drag for ice road"
I guess, it should cost < $500K, which is 1% of what such plane cost before the sanctions were put.

Seems like a very good plan. I wonder if it will happen exactly like that. Especially the smoothing and watering of the ground seems to me to be quite labour intensive. Do you recon it will take a lot of work?

@U_flow answered in the answer body, with some photos.

Out of curiosity, if the ice in fact dangerously slippery, wouldn't that likely actually be beneficial unless emergency braking was required?  Since the wheels on takeoff are essentially just there to support the plane.

@Chuu The wheels also provide steering, especially the ability to maintain one's lateral position on the runway surface in the presence of crosswinds.

Good answer. My only query I guess would be starting the plane when it's that cold, but I would guess that is a matter of portable generators and engine heaters? Would increase the costs of the operation but as stated, I guess by not a significant amount compared to the value of the aircraft.

@ThaRobster in Novosibirsk, aircrafts are often parked for night, and I guess they must be cold as ambient temperature by morning. I didn't hear from pilots that it takes some special equipment to cold start them. In the worst case, there are "heat guns" -- big tube, large like suitcase, with conducting spirals that heat up, and a big fan.

"And normal snow isn't slippery at all" - this is why I hate when they pour salt on footpaths here in the winter, it turns it into an dirty slush that ruins your boots, instead of the perfectly walkable packed snow.

Similar to Alrosa 514, TACA Flight 110 landed in grass. They repaired it on site (including an engine change), but were able to use a nearby road (which was previously a WWII-era runway) to make a short hop to a real airport. Their issue was more the short runway length than the surface, though.

@pipe Agree! When it's colder, snow+salt becomes like sand, never compacts, and is a lot harder to walk on.

@jcaron - TACA 110 had a little bit of room left over on landing, but not much as seen in this photo

you could almost walk on it upwards - I think the English phrasing you're looking for is "... walk uphill on it", if you were trying to make a frozen slope to slide down, but it came out not smooth.  ("walk on it upwards" isn't something we'd normally say in English, except maybe vertically upward like a spider :P)  Also, "if it's much lower than 0" might be clearer as "if it's far below 0".  The first phrasing makes it sound like 0 C is about where salt stops working.  Salt actually works ok down to about -9 C.  And from practical experience in Canada, ice is slippery down to about there.

@PeterCordes edited my post, thanks!

Cheers :)   (Correction to my previous comment: Salt works fine above about -9C, which is where it starts to work less well.  And works but not as well below that, until about -18C where it really doesn't work, according to some google results. I felt like my previous phrasing could imply -9 C was the lower limit; conveying the right connotations and implications can be tricky even for a native speaker!  Anyway, both these temps are pretty far below zero, and -18 is definitely far below 0, so that phrasing is good. :)

PS: another article (https://www.cbc.ca/news/canada/nova-scotia/dalhousie-university-professor-says-it-s-not-too-cold-for-road-salt-1.2960143) has some other numbers, like -12 C for the lower limit of when they salt the roads here in Halifax, and -21C as the melting point of water + sodium chloride; below that, other types of salt like calcium chloride could potentially still help, but less effectively.

@PeterCordes thanks for posting. As new urbanism activist, I was aware of anti-icer chemistry, because there's a big debate on this. Several years ago, I moved to live to St. Petersburg, and later to Moscow, and saw the cities use calcium chloride everywhere, and all the winter every sidewalk and floor in shops was covered with this snow-mud. That was awful to look at, and to my surprise winter shoes would last only one season. Unfortunately, in 2018 the anti-icer manufacturer lobbied it into every major city of Russia, so moving back later, I saw it applied too, just at lesser scale.

Update - it didn't work :-(
News reports as of January 12th 2024 say:

"Ural Airlines has decided to dismantle its stranded A320 in a field in Siberia, instead of trying to retrieve it.
The plane crash-landed in September 2023, but all passengers and crew were unharmed.
The airline initially planned to fly the A320 off the field but reconsidered due to risks and technical difficulties, ultimately deciding to scrap it for parts.

from here

Also here

The Ural Airlines Airbus A320 that was forced to land in a field is to be dismantled, according to new reports. ... A Russian aviation Telegram channel, said that after a thorough evaluation has been completed, the decision has been made to dismantle the plane for parts and not attempt to fly the Airbus A320 out of the field as was previously proposed.
Aerotime revealed that Ural Airlines pays farmer year’s rent for wheat field holding the stranded Airbus until spring 2024.
The Ural Airlines plane remains in the field just outside Novosibirsk, in southern Siberia, protected by 24-hour private security in a fenced off area.

My guess is the insurance company wouldn't cover the flight under the existing policy, requiring additional insurance for the flight. And I can imagine the lawyers cautioning about the risk of expensive lawsuits from the flight crew's family if it didn't work out. Even if as the accepted answer predicts the flight would have been relatively safe, comparing all of that to what they will presumably get paid from insurance by declaring it a loss, probably it just wasn't worth it. Not sure who gets the money from the sale of parts in these type of situations, maybe the insurance company.

High demand and low availablitiy of spare A320 parts must have played a role in this decision.
"We can try an interesting but technically challenging solution to preserve our wealth, and maybe learn a thing or two in doing that, or, who cares, we go after big money with a rapid export of parts from the field to the nearest airplane market-place". Looks like (western) Europe economic politics of the last 20 years :D

I wonder, @StevePemberton, if the airlines (or Airbus') test pilots would be covered in a situation like that. After all, as a test pilot, one's family has the reasonable expectation that you'll not make it back from any given flight. (Sure, probably more likely to live now than in the 1950s or 60s, but...)

@FreeMan - and of course the pilots themselves would have accepted the risk. But none of this would matter in a civil lawsuit which would be about about convincing a jury that there was willful disregard of risk for the sake of profit. Whatever caused the crash, the plaintiff's lawyer would attempt to prove that the airline should have foreseen this possibility and not attempted to save money by flying the plane out. The odds of this situation actually occurring and a lawsuit succeeding who knows, but lawyers giving advice tend to put an emphasis on non-zero risk and the possible implications.

It's possible the ground didn't freeze deep enough to make for a viable runway. The picture can't be older than late January, since the plane's fate was in the air until then, but the landscape appears to be just below freezing point.

Yes, sad news. Thanks for posting an update. Just a notice: the photo of dismantling is from 2020 crash-landing near Moscow. Fields around Novosibirsk are still under a lot of snow.


text:
Effective eating habits as a student pilot
I've recently started pilot training and Im searching for some advice regarding eating habits. Typically I fly for ~3 hours, however I limit my eating until after I am finished, as in my first day of training I felt very nauseous and became sick.
So to avoid nausea typically I eat half a banana/ few biscuits at most to carry me till around 3pm.
It has been a few weeks and I now realise my habits are unsustainable as I become too exhausted and tired to revise my day's practice and churn through theory study. I understand I need energy so I can remain functional but I am anxious that I won't be able to keep my food down. I haven't been travel sick in the past while driving or in a commercial flight.
I would appreciate advice or things you may have learned through experience as I fear my eating habits thus far are limiting me with my concentration and keeping up with my studies.
Thank you for your time to read this

Whatever you do, don't eat the fish!

Side note: a fighter pilot once told me that bananas are a great food to eat before flying, because they're one of the only foods that tastes the same coming back up as it does going down

Would it be okay to change "sustainable" to something like "effective" ?  I read in the HNQ and thought it was about pilots eating in a ecological sustainable way.

@Criggie I've taken the liberty of doing that since OP has already accepted an answer so might not be back immediately. I too had a vision of a grizzled 747 pilot worrying that it was his snacks which were causing climate change.

I've experienced motion sickness a over the years both on boats and in planes that I've been at the helm of. I can offer some general points that I try to follow to mitigate this with diet. If you really want to follow a tight flight diet you can always take your cue from the SR-71 pilots:

When the crewmembers began getting ready to get dressed in their
suits, they came down to the dressing room from the kitchen where they
had their high protein/low residue pre-flight meal of steak and eggs.
The steak and eggs were a crucial part of the flight because of the
high nutritional value it contained, which sustained the pilots for
their long flights.

The first point I'll make is that you need to experiment and find out what works for you — everyone's diet and tolerance may vary.

Avoid greasy foods: I do love a bacon egg and cheese in the morning but that's not a great idea before a day of unusual attitude recovery (I learned the value of Piper's "pilot relief window" the hard way with this one). I generally avoid greasy breakfast meats before morning flying and my $100 hamburgers rarely involve actual hamburgers.
Coffee: This is a tricky one. Many people drink coffee every day and subsequently not drinking coffee can be as much as a problem as drinking it. Coffee is a diuretic which can cause issues in light aircraft if you don't have a solution to that problem. You also need to understand how caffeine affects you over a long period of time. Crashing or being too jittery is never good in the cockpit. For flights I try to limit myself to a single 16 oz (or smaller) coffee with a bit of cream. This is a battle between keeping my stomach calm and making sure I don't get a pounding headache from not having coffee.
Bring snacks: My flight bag has a standard complement of power bars and the such, in a variety of flavors to keep myself nourished throughout a long flight or if I need something simple and quick right before a flight. I also include things like mixed nuts here and other typical camping style snacks. I generally avoid high sugar things like candy bars if I can, they tend to make a mess on hot days anyways. Be careful with your snack bar choice as some are quite high in sugar.
Stay hydrated: In the summer small planes are greenhouses and sweat is inevitable. I always fly with ice water and some kind of sports drink to keep myself hydrated. This is perhaps one of the most critical elements of my complement to staying focused and keeping motion sickness down.
The Day Before: Remember if your flying early in the morning your previous dinner is going to play into your nourishment while flying. As will your previous days hydration and general intake. Much like with your pre-flight weather watch happens days before a flight your physical factor prep should as well.

The last thought I'll leave you with is, "don't avoid eating". In my experience getting sick with something in your stomach is way more tolerable than getting sick on an empty stomach.
As others have mentioned, time in the plane will help you adjust and mitigate motion sickness.

A lot of new pilots get motion sickness starting out in light aircraft, and it goes away with repeated exposure. So, it's just a matter of toughing it out until you get used to it, or if you're unlucky, you don't and eventually you will have to quit. It's like sea sickness, which is similarly something you have to get used to if spending time at sea (called getting your "sea legs").
Lots of pilots are fine in normal flying, but you can get them upchucking pretty quickly if you subject them to some serious aerobatics, without letting them get acclimatized.
One thing that can help with becoming desensitized to motion is to spend time on a park swing, with the constant exposure to 0 G at each end of the arc of the swing (I've been flying since the 70s and I'll still get a bit nauseous after 15 minutes on a swing).
As far as eating goes, the biggest enemy of pilots is the sudden blood sugar drop from eating a high carb/low fat meal in the morning. The archetypal coffee and donut breakfast, for a pilot doing something intense like IFR flying, can be quite dangerous when the sugar/caffeine buzz wears off. Make sure breakfast and other meals have a good amount of fat and protein.
While getting desensitized to motion, I'd suggest eating smaller meals frequently through the day, every 2-3 hours or so, so you stay nourished and full, but don't have a big load of food on board at any one time. Not high sugar between meal junk snacks, but normal food broken up into smaller intervals.

A professional driver once said to ne that the biggest mistake a driver can make is having tea or coffee with a lot of sugar, because first it "pushes you up" quite a lot, but later "it lets you down" just as rapidly. I have my tea without sugar. You have to get accustomed to it, but it works (good coffee does not need sugar, and sugar doesn't make bad coffee any better).

Tea does not need sugar either. This may be a cultural thing.

Ppl like sweet, and in older times adding sugar was too much of a luxury for poorer societies, so it's also a sign of wealth.  So culture does come into it a bit.

@sehe well, good loose-leaf tea usually tastes great without sugar. When all I can get are tea bags, and I drink it with no additions, I'd have to lie to say I like it. But sugar isn't the only option; even unsweetened soy milk can make a bad tea much more enjoyable.

@U.Windl Coffee has 3x the caffeine of tea, about 40-60 mg vs 140-180 mg. Tea is about the same as a can of Coke. It's fat that smooths out the absorption of sugars. And sat fat is not bad for your health at all.  The paradigm of fat-clogs-arteries that has been "settled science" for 50 years was/is complete BS, rooted in a trash study by a man named Ansel Keys in the 50s, which cherry picked data to produce a shocking curve of HD rates and fat consumption among 7 countries. The Seven Nation Study. It made Keys famous in the early 60s. Bacon, eggs, butter are very healthy foods.


text:
At what point can Approach mode be engaged in an A320?
In my experience using Flightgear and other computer simulators, when flying an ILS approach on an A320, the approach mode can only be engaged at a certain point or later. What is this point, and why is it used?

Is this experience in a "game" simulation, a real simulator, or the real world?

Updated post based on comment.

I wondered if it was a game - that often means great simplification from Bianfable's answer, for example Infinite Flight allows engaging APPR mode at <=200KIAS and NAV1 tuned.

Yeah, it's FlightGear, and the aircraft itself is pretty accurate, with majority of systems (fuel, hydraulic, bleed, electrical) working. MCDU is also probably 80-90% functional. I'd say it is one of the better computer simulators out there.

The conditions for arming the ILS APPR mode are given in the FCOM:

Arming Conditions
The pilot arms the (ILS) APPR mode (LOC and G/S in blue on the FMA) by pushing the APPR
pushbutton on the FCU, provided that:

An ILS approach is selected,
The aircraft is above 400 feet RA,
The ILS and RA are available,
Go-around or takeoff or final mode is not engaged,
ILS frequency and course are identically set on both receivers.

(Airbus A320 FCOM - Autoflight - Flight Guidance)
These are just the technical limitations for when you can arm the APPR mode, not when you should. The FCTM has some more details on that:

INTERCEPTION OF FINAL APPROACH COURSE
When cleared for the ILS, the APPR pb should be pressed. This arms the approach
mode and LOC and GS are displayed in blue on the FMA. At this stage the second
AP, if available, should be selected.
If the ATC clears for a LOC capture only, the crew will press LOC p/b on the FCU.
If the ATC clears for approach at a significant distance, e.g. 30 nm, the crew should
be aware that the G/S may be perturbed and CAT 1 will be displayed on FMA till a
valid Radio Altimeter signal is received.
[...]
MISCELLANEOUS
The ILS or LS PB is to be checked pressed in the first stage of the approach. The
crew will check that

LOC and GS scales and deviations are displayed on PFD
IDENT is properly displayed on the PFD. If no or wrong ident displayed, the crew
will check the audio ident.

(Airbus A320 FCTM - Normal Operations - ILS Approach)


text:
Best Way to certify DO-178 Communications Stack?
We currently have a piece of hardware running an RTOS that needs the communication stack to be certified to DAL-B. Everything has already been developed for non commercial aerospace applications, although we now have a commercial aerospace customer who is interested in our solution.
The communications stack handles a variety of different communication methods, and we're deciding on a make vs buy decision. These communication methods include ARINC 429, RS422 and Ethernet.
Are there any products out there that are DO-178 certified and handle these communication protocols? Or will we need to go through the certification process for our own implementations?

I'm not sure "best way" is answerable, but given the body of your question, it seems just a matter of differently phrasing the title.

Which RTOS? Is it certified already?

A. I don't know of any that can be purchased. Everywhere I worked, we developed our own. B. Even if you find one, you still have to integrate into your product and certify your product. Having a purchased stack would provide some certification documentation but it would not be complete for your application. C. I suggest hiring a Consultant DER. You can find one in the FAA Consultant DER Directory. Hiring an expert will save you time and money.

As @Gerry stated, it sounds like at least talking with a Consultant DER is the place to start, as showing compliance to DO-178C is no small task.

@selectstriker2 Real Time Operating System.

@JuanJimenez, yes, but which one?

@selectstriker2 You changed your comment, and if you now want to know which RTOS is being used you should ask the poster, not me...

@JuanJimenez, my original comment was never edited, and I was asking the OP which one. I should have looked better at your response, as I thought it was coming from the OP


text:
Does anyone recognise this jet engine?

sorry for the terrible quality, it's what I've got. I've not been able to find anything looking like it using google image search. It looks too detailed for a random bit of clip art.
Possibly around 12-15 feet long by 2-3 feet diameter

where have you found that image? in what context?

it's an image that was pasted into a line drawing of an experimental apparatus. Bits of it may have been modified @Federico I'd be interested to know where the image originally came from too.

looks more like a generic "this is a jet engine" picture than anything indicating a specific model.

that could well be @jwenting, it just looked like a few too many McGuffins - although they're quite tame by real engine standards.

You'll need looking at Jane's, they publish yearly about aircraft engines, or in the work by Ricard Miguel Vidal: 'El motor de aviación de la A la Z', free and open access for AEHS members. Salut +

I accepted my answer as I believe it is correct, and don't want to pollute the unaccepted answers pool, but I will happily accept anyone else's better answer.

I think it's a fairly good match for the Rolls Royce F405 Ardour. I can't quite work out which version though....
Thanks to everyone who spent time looking.
Rolls-royce.com
here's an afterburner and nozzle for a variant:
Hunini


text:
Round or sharp separation edges for lower drag?
Two same object,only difference is in separation edges,one has round ,other has sharp edges.
Round edges decrease wake but edges itslef produce low pressure because of curvature.
Sharp edges increase wake but dont produce low pressure like round edges.
Which type of edges is better for lower drag? Object is 5m long..

Do they really?  The trend seems to be towards rounding the trailing edges, but it may have much to to with velocity of the airstream over the surface and where the turbulence begins.  It seems (in wind tunnel tests) that the shape of the airflow can matter is much as the shape of the object.

Well they don't always use sharp edges, but whenever possible they do.

It might be a weight/parking clearance best compromise, but the Wrights(with their wind tunnel) seemed to like a little rounding at the trailing edge tips.

Which size are you talking about 10cm, 20m? What is the section?

Don't say it is a car, this is Aviation Stack Exchange

The car industry uses the shapes they do for a reason. A clean separation with sharp edges as presented in the picture produces less drag than letting the airflow follow a conture that turns it drastically.
In aviation it is preferred to use fairings to "strech shapes that would otherwise present the dilemma mentioned in your question. Therefore this is not that much of an actual consideration in  aircraft design.
These fairings transform the shapes such, that the radius of the terminating shape is in the order of magnitude of centimeter (fuselage, engine pods and such) or millimeters (wings, flaps, ailerons etc.). In these scales the sharpness may present more problems than advantages, mainly from manufacturing point of view: for example for aluminium construction sharp edges are not desirable, as they are structurally prone to failure.


text:
Does closed oval wing produce two vortex and downwash between them, like normal wing?
Does closed oval wing like this in video produce two vortex and air between them goes in downward direction like on normal wing?
I think yes ,because cause for downwash is wing that push air down, not wingtip vortex.
Some members here write that two wingtip vortex is cause for downwash.

The "as dupe" thread doesn't really address this sort of wing, and the differences between the box-wing and this one seem at least potentially enough to cause different dynamics here. IMHO, this question is sufficiently distinct to warrant its own answer. Voting to leave open.

A trailing vortex leaves the wing at each point where the wing's circulation (which is proportional to lift coefficient times chord) has a gradient over span. Only an infinite wing has no induced drag because its circulation is constant over span. "Hiding" the wingtips by using an oval wing is similar to closing your eyes so you don't see the approaching train - just as the train comes closer anyway, the wing sheds a vortex sheet. Basically, the oval wing is a biplane, so its two sides interfere just like the two wings of a biplane, reducing its overall efficiency. And not adding bracing means forfeiting the structural benefits of a biplane.
It's sad to see that some people still refuse to learn.

"It's sad to see that some people still refuse to learn." Members are not problem, problem is 90% books  describe wrong everything about wingtip vortex topic, I often read how wingtip vortex cause induced drag...

@JurgenM Its obviously the people who put much work into a dud of a concept. Don't take things personally that are not meaning you. And you are right about 90% of those books out there. –

Given that the aircraft supports itself by accelerating air downwards, how could those vortices not exist?
At a large scale, the air movement around a heavier-than-air aircraft takes the form of a torus, with air moving downwards in the middle and upwards at the periphery.  In practice this torus is typically highly distorted because the aircraft is moving quickly and the air moves relatively slowly.  A conventional wing tends to concentrate the rotation at the wingtips, resulting in a tight vortex with relatively high airspeeds and therefore sapping a significant amount of energy that isn’t directly contributing to generating lift.  There are several ways to mitigate this, such as washout, tip plates, and closed oval wings; to differing extents these make the vortices less concentrated and so the air circulates less quickly and saps less energy.

Thanks I shall add some more explanation.


text:
What CAD software is most commonly used for aircraft design?
What is most commonly used CAD software for aircraft design?
AutoCAD, CATIA..?

Why down voted? This user isn't asking for "recommend me software" rather he is asking for commonly prevailing design software in industry.

I didn't vote @viktor - but they asked "what is best" - that's going to require an opinion - unless the answer is just "at Boeing we use X, Y, Z"  If the question was more general it wouldn't need an opinion based answer - or even just "what CAD software is used" ...

It really depends upon what you’re designing or analyzing, and what company you work for. In regards for structural design, at the major OEMs, CATIA V5 and V6 are the most common.  This is particularly true for transport category aircraft. for example the Boeing 787 and 777X structures are all designed in CATIA.  The defense and space business is a mix of CATIA and NX, with NX the preferred software for many space startups.  Solidworks is commonly used by third party vendors and, strangely enough, popular with Scaled Composites.  Cirrus designs all of its light normal category aircraft in PTC CREO.
What I would recommend is learn one particular type of parametric, feature-based, solid modeling software and you can use that as a springboard to other software types.  If you can afford to take a course on a particular software app, feel free to do so, though they can become expensive. They are usually offered a standard curriculum at a major engineering department at a university.


text:
When was the word "aerodynamics" first used?
Aerodynamics comes from two Greek words: aer (air) and dinamike (dynamics).
In this link it says

The word “aerodynamics” itself was not officially documented until 1837

I don't know if that is correct. Did Sir George Cayley first use/invent this word or maybe Isaac Newton when he study the two external forces that operate
on fluids, viscous shear friction and pressure?

OED also has 1837 as the first citation, but that's in an encyclopedia so not a novel coinage. It might well have been Cayley, but without written sources we'd just be speculating.

That's better than google ngram viewer, which around then gives only one hit, in 1841.

In French, the word appeared in print in 1784 in a journal, Journal de l'Orléanois. In an article, the Société Royale de Physique d'Orléans, created 25 years ago, describes the different branches of mechanics to potential scholars. None of these branches seems to be a recent field:

Source: BnF
In a time following Les Lumières, the word was necessarily shared among European scientists, particularly those with a strong scientific culture. This would include England and its Royal Society, long before 1837. For reference, John Smeaton, a fellow of the Royal Society, described drag (Smeaton coefficient) in 1759 in Natural Powers of Water and Wind to Turn Mills and Other Machines Depending on Circular Motion.
In France, aérodynamique found an official definition in 1835, in the technical supplement, published by lexicographer François Raymond, to the dictionary published by the authoritative Académie française. .

Source BnF

Maybe Isaac Newton when he study drag?

@user707264: There is also Mariotte's prior work on drag, but they may have not used the term aerodynamics

In German, the word Aerodynamik is in print by 1780 in the Deutsche Encyclopädie oder Allgemeines Real-Wörterbuch aller Künste und Wissenschaften vol 3 under the entry for Baumeister (a builder / architect).
It also uses the newly-coined words Aerostatik, Hydrodynamik and Hydrostatik, and here is principally concerned with the effect strong winds can have on buildings.

Die Aerostatik und Aerodynamik zeiget uns dei Größe des Windstoßes
auf die Gebäude und deren Theile, durch deren Vernachlässigung schon
viel Schaden geschehen — die Schwere und Würkung der Luft

SOURCE
In English the The Penny Cyclopaedia of the Society for the Diffusion of Useful Knowledge published in London in 1833 has an entry for AERO-DYNAMICS. It also uses the word without a hyphen, so this is an earlier example than the Oxford English Dictionary provides.

SOURCE


text:
Does pilot need to increase thrust when gust hit him at landing and where is axis of rotation?
Let's say a plane is flying above a runway in straight line, and gust of wind hits the plane from side.
Do pilot need increase thrust to stay above runway and where is axis of rotation ?
It often said that all object rotate around c.g. does it mean that axis of rotation passes through plane c.g. or somewhere else?
My interest is from the view of an observer seeing this encounter standing under the plane - a view from a ground-based frame of reference.

What are you trying to get from the answer? Because the gust of wind will cause the aircraft to change it attitude but it will also change it speed vector. So there will be a combination of rotation and translation. The combination will not necessarilly scale linearly with the magnitude of the gust. And in which reference frame do you want to define this axis? The aircraft moves with respect to the earth and with respect to air. Do you want to define the axis in the aircraft frame of reference, the earth frame of reference or the air frame of reference?

@DeltaLima ref. frame earth

"gust of wind hit plane from side" what does it mean from side? Suddenly the whole side surface? Only the tail? Only the nose? Is it an assignment? What's your opinion?

@sophit yes all surface

Adding thrust will cause the plane to rise.  Pilots generally increase bank to hold against wind.  But for planes with very long wings, there is a danger of wing tip strike.

By a physics point of view it can be demonstrated that the movement of a rigid body (like an aircraft) can always be represented as the sum of a translation plus a rotation of its centre of mass. So yes, due to the gust, the airplane is going to rotate around its center of mass and its center of mass is going to shift. How exactly depends on how the gust looks like.

@RobertDiGiovanni But when gust hit, plane is blown downwind from runway?

@user628075 yes, of course, and if your plane rotates into the wind adding thrust will help you hold line.  But why do that when sideforce can be created by banking?  Thrust will increase your airspeed.  The plane won't want to land.

The aircraft doesn’t rotate around a particular axis, it will be blown downwind and will rotate, so you can choose any axis that’s meaningful to you.  The centre of gravity might be useful in many cases.

plane change orientation so it must rotate around some  axis

Relative to the ground, the axis will be a long way ahead of the aircraft and will move relative to both the ground and the aircraft, but this is unlikely to be useful to identify for any practical purpose.


text:
"Pure" Aerospace engineering vs mechanical engineering/pathway aerospace?
Does "pure" aerospace engineering give better aero-knowledge then mechanical engineering/pathway aerospace?
What is point of specialization aerospace at mechanical engineering, isn't aerospace too big branch to be just one pathway?

It really depends on what you want to do in the business. If you’re looking at jobs as an aerodynamicist, or flight, test, work, or similar specialized aeronautical or space work, then an aerospace engineering degree would probably make more sense. For general work i.e., structural design, structural analysis, that sort of thing, a Mechanical Engineering degree is just fine.
That being said, much of the specialized knowledge you need can be obtained after school through trade groups, lobbying organizations, such as SAE, AIAA, etc.
Fresh out of school, I believe an employer is going to look at 1) your overall performance in school ie GPA, what you majored in ability to handle difficult subjects, etc. 2) internships and class projects.  If those tend to be in line with what they’re looking for in entry-level work, you have a good chance of getting in.
Aerospace has become considerably easier to enter into as a new engineer than it has in the past. This is largely due to the fact that employers have shot themselves in the foot for years relying on senior guys with a lot of experience, and neglecting the tribal knowledge aspect of the profession to mentor and bring in new people. They’re now backed up against the wall and facing a brain drain as senior employees retire, so there’s considerable motivation to bring in and mentor young people.
If you’re living in the United States, far more integral to job security would be the ability to obtain a security clearance. It would not only guarantee local work, but also high pay work.  So don’t get yourself into a lot of debt, don’t use drugs or commit crimes, or anything else that would potentially deny you such a clearance.

Aerospace companies of all kinds and sizes hire lots of engineers of all kinds -- Mechanical, Electrical, Software, etc.  Anyone with a technical background who wants to work in the Aerospace industry should be able to find a role.
Mechanical Engineering's curriculum is the closest cousin to Aerospace Engineering, so your question about 'whats the difference' is a relevant one.
ME curriculum does not focus on any particular industry -- they'll work manufacturing (of anything), mechatronics, HVAC, automotive, etc. etc.  However, in Aerospace, the curriculum is focused on flight vehicles -- aircraft (airplanes, helicopters, gliders, etc), launch vehicles, orbital spacecraft, space probes, etc.
What this means is that the ME's do not consider the vehicle as a whole -- it is a bunch of mechanisms, components, and machines all working together.  Conversely, AE's are always interested in the system as a whole -- that is usually the vehicle, but it can also be the fleet, constellation, or other even larger system.
A good example of this is typical Sr. Design curriculum.
In a ME program, it is expected that a Sr. Design project start with a problem statement and proceed through the design process until fabrication and test.  You have to build it or it doesn't count.
Conversely, in an AE program, it is expected that a Sr. Design project consider the entire aircraft or spacecraft.  Since the real system at scale may take years and $1B to develop, you clearly can't do that in a university course.  So instead of going all the way to building it, most AE Sr. Design program's final output is a report about the design of the aircraft -- a paper aircraft.  If you don't do the whole system, it doesn't count.
In ME, they would never accept a paper about designing a widget if you don't build the widget.  In AE, they would never do a design of a widget, you have to do the whole vehicle or more.
Some AE programs try to compromise and have students build a R/C aircraft or UAV.  This can be done in a way that it is a surrogate for a design of a full aircraft system, but often there are many compromises in this approach.
In industry, you'll find that most of the jobs that have a full vehicle, big picture, or system-level perspective are filled with Aerospace Engineers.  In fact, you'll find that when other industries need systems-thinkers, they often hire Aerospace Engineers to do decidedly non-aerospace things.
None of this is to say that there aren't exceptions -- I know Civil Engineers and Architects who ended up as Technical Fellows in Conceptual Design.


text:
Why induced drag shows up as reduced pressure downstream of the wing?
Quote from  book  (Understanding Aerodynamics: Arguing from the Real Physics, Doug Mclean):
"When we look at the force/momentum balance, the induced drag shows up in the flowfield primarily  as reduced pressure downstream of the wing.."
Which pressure is reduced downstream of the wing, dynamic pressure (measured by aero-rakes)?
Downward flow around the wing cause induced drag, so higher the speed of that flow, induced drag is higher and more reduction in dynamic pressure behind the wing?

The quote does not appear to be symbiont within the text I reviewed.  On what page does this quote appear?

In a wind tunnel, drag shows up as a reduction of the speed (momentum to be precise) of the airstream behind the body.
The drag that normally appears in any plot of the aerodynamic coefficients, is determined exactly by measuring this speed reduction, which is termed momentum deficiency. This momentum deficiency is what the engine has to supply to keep the aircraft flying.

Which pressure is reduced downstream of the wing, dynamic pressure (measured by aero-rakes)?

As you have correctly guessed, the momentum deficiency is measured by aero-rakes behind the body. Integrating the difference in the total pressure from the aero-rakes with respect to the total pressure measured in front of the body, the aerodynamic drag can be calculated.
It should be clear now that, in a wind tunnel, only the total aerodynamic drag can be measured and not each and every component making it up: parasite drag, induced drag, viscous drag, ... you name it. So, induced drag cannot be really measured, it can only be estimated mathematically by means of its definition.

So higher the speed of that flow, induced drag is higher?

Induced drag is defined as:
$D_i = \frac{L²}{½ \rho V² \pi e b²}$
All the rest being the same, a higher speed $V$ gives a lower induced drag.


text:
Can I reduce drag with channeling freestream air at the backward facing surface?
Idea is to increase static pressure at backward facing surface to reduce drag.
Can I reduce drag with channeling freestream air  at the backward facing surface, like picture suggest?

I suppose there would be a so big pressure loss in the pipes virtually neglecting any benefit

Is the flow within those pipes turbulent? How much drag happens within them? The wing works by having lower pressure above the wing than below, but this drawing seems to introduce air of equal pressure to both top & bottom, which ought to reduce total lift, requiring more AoA to compensate. Not seeing the positive value here, unless I'm missing something.

you're basically reinventing the slotted flap https://aviation.stackexchange.com/questions/30960/how-does-the-slotted-flap-work

You're sort of close conceptually, but from a practical point of view taking space from the fuselage or wing structure for plumbing may not work out.
But this thinking is on the right track.  The rearward portions of aircraft structure are where the boundary layer can become more and more turbulent, increasing drag.
"Blowing" these regions can lead to reductions in drag, leading to improvements in fuel economy.
Props have been mounted on the trailing edges of wings and/or fuselage, and jet engines placed on aft portion of the fuselage can also help "clean up" the air flow.
Related reading here.  Application: drag reduction high speed trains.